Give the necessary conditions for total internal reflection.
The correct answer and explanation is :
Correct Answer:
Total internal reflection occurs when both of the following conditions are met:
- Light travels from a denser medium to a rarer medium (i.e., from a medium with a higher refractive index to one with a lower refractive index).
- The angle of incidence is greater than the critical angle for the pair of media involved.
Explanation (Around 300 Words):
Total internal reflection (TIR) is an optical phenomenon that occurs when a light ray traveling within a medium (like water or glass) reflects entirely back into the same medium instead of refracting into the second medium. For this to happen, two critical conditions must be satisfied:
1. From Denser to Rarer Medium:
The light must move from a medium with a higher refractive index (denser) to one with a lower refractive index (rarer). For example, light traveling from water (n ≈ 1.33) into air (n ≈ 1.00) or from glass into air.
This direction is important because only in this configuration can a critical angle exist. If the light is moving from a rarer to a denser medium (e.g., air to water), total internal reflection cannot occur, regardless of the angle.
2. Angle of Incidence Greater than Critical Angle:
The critical angle is the angle of incidence at which the refracted ray just grazes along the boundary, making an angle of 90° with the normal. It is given by:
[
\theta_c = \sin^{-1}\left(\frac{n_2}{n_1}\right)
]
Where ( n_1 ) is the refractive index of the denser medium, and ( n_2 ) is that of the rarer medium.
If the angle of incidence exceeds this critical angle, the refracted ray no longer exists; instead, all the light reflects back into the denser medium — this is total internal reflection.
TIR is the principle behind technologies like optical fibers, prisms, and even sparkling effects in diamonds, where light is trapped and guided by repeated internal reflections.
